include("RepSt.jl")

testing......done.

Main.St

# Some morphisms in RepSt.
id1 = St.id(1)
dots = St.dots
id2 = St.id(2)
transposition = St.cross
H = St.box
St.show([id1, dots, id2, transposition, H])
St.show(St.make.([ [1 2 1; 1 2 1], [1 2 1; 3 2 3], [1 2 2; 2 2 1] ]))

, , , ,

, ,

# Composition in RepSt.
# Caution: * is top to bottom, and showComposition(a, b) shows the composition (ba)!
showComposition(a, b) = St.show([St.formalProduct(a, b), "=", St.mult(a, b)])
showComposition(id1, dots)
showComposition(dots, dots)
showComposition(id2, transposition)
showComposition(transposition, transposition)
showComposition(transposition, H)
showComposition(id2, H)

* =

* = t

* =

* =

* =

* =

# An element in the monoidal center
sigma = [2, 1] # a permutation in S_2
halfbraiding = St.makeC(sigma)
St.checkbraidingC(2, halfbraiding)

---- check braiding ----
k = 2; c1 = 

+ + - -

...
[OK] mult(hom01, ed1) == mult(hom01, e1)
[OK] mult(hom10, ed1) == mult(hom10, e1)
[OK] mult(crossk, ed2) == mult(ed2, crossk)
[OK] mult(boxk, ed2) == mult(ed2, boxk)

# Okay, let's tune it up: sigma = (1 2 3) in S_3
St.checkbraidingC(3, St.makeC([2, 3, 1]))

---- check braiding ----
k = 3; c1 = 

+ + + - - -

...
[OK] mult(hom01, ed1) == mult(hom01, e1)
[OK] mult(hom10, ed1) == mult(hom10, e1)
[OK] mult(crossk, ed2) == mult(ed2, crossk)
[OK] mult(boxk, ed2) == mult(ed2, boxk)

# ... and sigma = (1 2 3)(4 5) in S_5
include("RepSt.jl")
St.show(St.makeC([2, 3, 1, 5, 4]))

testing......done.

WARNING: replacing module St.

+ + + + + - - - - -